I have a Dometic Airrr system in my 2004 Mainship Pilot II.
It seems to be cooling well, but it cycles on and off very often.
Also, the temperature reading seems to be higher than the actual cabin temp.
When the unit is running I can check the AC outlet vents with my laser temp gun and it reads around 45 degrees, which I'm told is good.
I have to set the cabin temp to around 67 degrees to get it to feel comfortable inside. When the unit reaches this temp, it cycles off, which seems normal, but then it will cycle on and off at approximately 15-30 second intervals to maintain
the temp.
Since the unit is under our berth, it is difficult to sleep with the constant cycling.
The raw water pump seems to be operating normally.

Someone suggested the thermostat may be bad. Any thoughts are appreciated.

I have a Dometic Airrr system in my 2004 Mainship Pilot II.
It seems to be cooling well, but it cycles on and off very often.
Also, the temperature reading seems to be higher than the actual cabin temp.
When the unit is running I can check the AC outlet vents with my laser temp gun and it reads around 45 degrees, which I'm told is good.
I have to set the cabin temp to around 67 degrees to get it to feel comfortable inside. When the unit reaches this temp, it cycles off, which seems normal, but then it will cycle on and off at approximately 15-30 second intervals to maintain
the temp.
Since the unit is under our berth, it is difficult to sleep with the constant cycling.
The raw water pump seems to be operating normally.

Someone suggested the thermostat may be bad. Any thoughts are appreciated.

From the manual
"Program Cool only and cooling only will be supplied. Thecabin temperature will be maintained within 2°F (1.1°C) of
set point. "

"P-5: Temperature Calibration
Use this feature to calibrate the ambient sensor. Select P-5
and the ambient temperature appears in the display. Use
the Up and Down Buttons to set the correct reading. The
temperature in the display will increase or decrease as
required. "

If the unit has a low suction cut off the unit would cycle as described for a few reasons. If the filters are extremely dirty or something else is restricting air flow like closed dampers or a crushed supply duct. The unit would also do this if it was low on refrigerant. If the unit does not have a low suction limit then the above does not apply.

If the unit cools normally to its set point, then it is unlikely a refrigerant problem. There may be a 'remote' thermostat sensor that is dangling somewhere in the air flow path. The remote sensor is the primary sensor and will override the sensor in the control unit on the bulkhead. If like mine, the remote sensor was taped directly in from of the unit's air intake under the bed. Mine was being impacted by hull temperature. Unplug the sensor from the circuit board and control will shift to the bulkhead control unit sensor. Then you can calibrate the control unit per Don's suggestion.